Margin of Error Basics Quiz (HSS.IC.A.1)

1) Best interval?

48–52

46–54

50–58

54–62

54 ± 4 → 50–58.

Explanation

54 ± 4 → 50–58.

2) Statistic vs parameter?

Parameter known

Statistic from sample; parameter fixed for pop

Statistic theoretical

Both sample

Statistic from sample; parameter true value.

Explanation

Statistic from sample; parameter true value.

3) Poll X: 49% ±2, Poll Y: 48% ±2. Conclusion?

X preferred

Too close

Y preferred

Add margins

Intervals overlap.

Explanation

Intervals overlap.

4) Survey reports ±7%. Best statement?

Unusable

Measures fairness

True value likely within 7 points

Statistic equals parameter

±7 means true value likely within 7 pts.

Explanation

±7 means true value likely within 7 pts.

5) Largest MOE?

1,000 people

5,000

150

2,000

Smallest sample → largest MOE.

Explanation

Smallest sample → largest MOE.

6) Why MOE important?

Shows who is winning

Eliminates variability

Proves no bias

Shows estimate uncertainty when close

MOE matters when numbers close.

Explanation

MOE matters when numbers close.

7) Meaning of 95% confidence?

95% respond

95% honest

Method captures true value 95% of samples

True value 3% away

Meaning of confidence.

Explanation

Meaning of confidence.

8) If confidence increases, MOE:

Decreases

Same

Zero

Increases

Higher confidence → bigger MOE.

Explanation

Higher confidence → bigger MOE.

9) To reduce MOE:

Increase sample size

Use convenience

Raise confidence

Survey fewer

Increase sample size.

Explanation

Increase sample size.

10) Based on MOE what conclusion?

Guaranteed pass

Likely majority but could be near 50

No uncertainty

Statistic equals parameter

Interval includes values near 50.

Explanation

Interval includes values near 50.

11) A news poll reports: “52% support the new policy, margin of error ±3%.” What is the best interpretation of the margin of error?

The estimate could reasonably differ from the true population proportion by about 3%

The true population proportion is exactly 52%

The sample size is too small to trust the result

The poll is guaranteed to be within 3% of the truth

Margin of error tells how far the sample result might be from the true population value.

Explanation

Margin of error tells how far the sample result might be from the true population value.

12) Which factor MOE depends on?

Sample size

Population size

Number of questions

Demographics

MOE mainly depends on sample size.

Explanation

MOE mainly depends on sample size.

13) Survey finds 40% ± 8%. Best statement?

Exactly 40% prefer

True is 38–42

Sample biased

True is 32–48

40 ± 8 → 32 to 48.

Explanation

40 ± 8 → 32 to 48.

14) If sample size doubles, MOE generally:

It doubles

Same

Decreases

Unpredictable

Bigger sample → smaller MOE.

Explanation

Bigger sample → smaller MOE.

15) Two polls MOE ±3% and ±5%. Which is more precise?

Poll B safer

Poll A more precise

Poll A has larger population

Poll B used more questions

Smaller margin → more precise.

Explanation

Smaller margin → more precise.

16) A campaign reports 60% ± 2%. Best statement?

Estimate within 2 points

Candidate will get 58–62

Sample equals population

MOE measures bias

Means true support likely 58–62.

Explanation

Means true support likely 58–62.

17) Which is a sample statistic?

True avg height of all students

Entire voter list

Actual proportion of all voters

Average of 200 students

A statistic is calculated from a sample.

Explanation

A statistic is calculated from a sample.

18) What does the population parameter refer to?

The true value in population

Number of respondents

Statistic from sample

Margin of error

A parameter is the true value.

Explanation

A parameter is the true value.

19) Which change generally reduces the margin of error?

Using a convenience sample

Increasing variability

Decreasing confidence level

Increasing sample size

Larger sample → smaller margin.

Explanation

Larger sample → smaller margin.

20) In a poll with margin of error ±4%, the sample proportion is 46%. Which interval best represents the plausible range for the population proportion?

40% to 44%

42% to 50%

44% to 52%

46% to 54%

46% ± 4% → 42% to 50%.

Explanation

46% ± 4% → 42% to 50%.

Understanding Margin of Error Concepts Quiz

1) Best interval?

2)

What first name or nickname would you like us to use?

2) Statistic vs parameter?

3) Poll X: 49% ±2, Poll Y: 48% ±2. Conclusion?

4) Survey reports ±7%. Best statement?

5) Largest MOE?

6) Why MOE important?

7) Meaning of 95% confidence?

8) If confidence increases, MOE:

9) To reduce MOE:

10) Based on MOE what conclusion?

11) A news poll reports: “52% support the new policy, margin of error ±3%.” What is the best interpretation of the margin of error?

12) Which factor MOE depends on?

13) Survey finds 40% ± 8%. Best statement?

14) If sample size doubles, MOE generally:

15) Two polls MOE ±3% and ±5%. Which is more precise?

16) A campaign reports 60% ± 2%. Best statement?

17) Which is a sample statistic?

18) What does the population parameter refer to?

19) Which change generally reduces the margin of error?

20) In a poll with margin of error ±4%, the sample proportion is 46%. Which interval best represents the plausible range for the population proportion?